Catcher Gary Sanchez after fourth inning home run, is fulfilling...

Catcher Gary Sanchez after fourth inning home run, is fulfilling the promise on both sides of the ball the Yankees saw 10 years ago. Credit: Kathleen Malone-Van Dyke

Ten years ago on Thursday, the Yankees signed a 16-year-old catcher out of the Dominican Republic. That teenager was Gary Sanchez.

The Yankees didn’t unearth some skinny kid and turn him into an All-Star. The story is much less dramatic than that.

Sanchez was well-built, well-known and well-scouted. Someone was going to sign him for a lot of money. The Yankees got the signature for a reported $3 million bonus.

It hasn’t been a straight road to stardom, as it seldom is. There have been injuries and immaturity and passed balls. A lot of passed balls.

But Sanchez, at age 26, is fulfilling the promise on both sides of the ball that the Yankees saw 10 years ago.

“He’s a great player and a really talented player,” manager Aaron Boone said before Sanchez went 2-for-5 with his 22nd home run in the Yankees’ 10-6 win over the Astros. “Sometimes as a young player, you can go through some struggles. Actually, forget ‘young player.’ This is a hard game, and especially at a position like catcher . . . Sometimes there’s some growing pains that goes with that. You’ve got to allow for that growth. I think what we’ve seen from Gary, through all the success that he’s had, through all of the struggles he’s had, [is] that he’s grown from it. He’s gotten better from it. He’s matured from it.”

At soggy Yankee Stadium on Thursday night, Sanchez started behind the plate for the fourth consecutive day. He was in the third spot in a lineup that is one day away from being whole with Aaron Judge set to return from the injured list on Friday.

On his first trip to the plate, Sanchez banged a single off the bottom of the rightfield wall. It wasn’t one of those “singles that should have been a double” because Sanchez loafed down the first-base line. In fact, he booked it out of the box, but the ball was hit so hard that stopping at first was the only option.

It was the Yankees’ only hit against Astros lefthander Framber Valdez until Sanchez led off the fourth in a scoreless game with a 402-foot home run to left. Sanchez’s 22nd home run tied him for the American League lead with Mike Trout and new teammate Edwin Encarnacion (who hit his 23rd in the seventh).

Sanchez’s homer opened the floodgates in more ways than one. Soon after he gave the Yankees the lead, a heavy rain started falling. Gleyber Torres later hit a three-run homer through the teeth of the deluge to give the Yankees a 4-0 lead.

The rain stopped, and DJ LeMahieu hit a two-out, two-run homer into Monument Park off Chris Devenski to make it 6-0.

After Luke Voit singled, Sanchez returned as the 10th man to bat in the inning. The rain returned, too, and play was halted at 8:36 p.m.

When play resumed 37 minutes later, Sanchez hit a first-pitch dribbler to first to end the inning.

Sanchez has 50 RBIs and a .963 OPS. Both figures lead the team, and that’s after he spent April 12-24 on the IL with a strained left calf.

Sanchez hit .186 in 89 games last season. He was on the disabled list twice because of a groin strain and had shoulder surgery after the season. At times his defense was atrocious. It was legitimate to ask if he was always hustling, and it would have been understandable if the Yankees started to sour on the idea of Sanchez as an everyday catcher.

They did not. They are reaping the rewards of their faith and patience. Sanchez should be the starting catcher for the American League in the July 9 All-Star Game in Cleveland.

More importantly for the Yankees, he is hitting home runs and blocking balls and running hard to first — well, most of the time.

On that dribbler after the delay, Sanchez stayed at the plate a second before jogging a few steps toward first. Baby steps, you might say. But the Yankees are used to them.

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